The Reduced Basis Method for an Elastic Buckling Problem

Lorenzo Zanon, Karen Veroy

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

In this work, we apply the Reduced Basis (RB) Method to the field of nonlinear elasticity. In this first stage of research, we analyze a buckling problem for a compressed 2D column: Here, the trivial linear solution is computed for an arbitrary load; the critical load, marking the transition to nonlinearity, is then identified through an eigenvalue problem. The linear problem satisfies the Lax‐Milgram conditions, allowing the implementation of both a Successive Constraint Method for an inexpensive lower bound of the coercivity constant and of a rigorous and efficient a posteriori error estimator for the RB approximation. Even though only a non‐rigorous estimator is available for the buckling problem, the actual RB approximation of the output is more than satisfactory, and the gain in computational efficiency significant. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Original languageEnglish
Title of host publication84th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM, Novi Sad, Serbia, March 18-22, 2013)
EditorsL. Cvetkovic, T. Atanackovic, V. Kostic
PublisherWiley-VCH Verlag
Pages439-440
Number of pages2
DOIs
Publication statusPublished - 29 Nov 2013
Externally publishedYes
Event84th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2013) - University of Novi sad, Novi Sad, Serbia
Duration: 18 Mar 201322 Mar 2013
Conference number: 84

Publication series

NamePAMM, Proceedings in Applied Mathematics and Mechanics
Number1
Volume13
ISSN (Electronic)1617-7061

Conference

Conference84th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2013)
Abbreviated titleGAMM 2013
CountrySerbia
CityNovi Sad
Period18/03/1322/03/13

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